Advance Praise

“[A]n engaging meditation on complexity and on how living things often unwittingly use math to navigate it.”—Scientific American

“This remarkable book gives the lay person a sense of subtle problems in mathematics and artificial intelligence, and offers a framework for biologists and computer scientists to use in jointly investigating the most fascinating and enigmatic biological questions.”—Marc Kirschner, Professor of Systems Biology, Harvard Medical School, and coauthor of The Plausibility of Life

“This book contains fresh thinking and elegant, nuanced ideas. It is more than probably approximately brilliant. Anyone interested in computation, learning, evolution, or human nature should find these pages extraordinarily stimulating and informative.”—Stephen M. Kosslyn, Founding Dean, Minerva University, and former Professor of Psychology, Stanford University

“Probably Approximately Correct is a great book. It was eye-opening to me, as a mathematician, to learn how we think and reason, and as a grandfather, to understand better the development and learning of my four-month-old grandson. Valiant’s book offers deep insights, both for young and old.”—Shing-Tung Yau, Professor of Mathematics, Harvard University, and coauthor of The Shape of Inner Space

“Ecorithms are algorithms that learn from interaction with their environment. This book provides a theoretical framework for understanding the power and limits of ecorithms and applies it to human cognition, biological evolution, and artificial intelligence. Elegantly written, it will be accessible to a wide circle of readers.”—Richard Karp, Turing Award winner and director, Simons Institute for the Theory of Computing, UC Berkeley

“The quest for machines (and codes) that never make mistakes was only a first step toward machines (and codes) that learn from them. Probably Approximately Correct is a detailed, much-needed guide to how nature brought us here, and where technology is taking us next.”—George Dyson, author of Turing’s Cathedral

“This ambitious little book suggests quantitative, mathematical theory to explain all essential mechanisms governing the behavior of all living organisms: adaptation, learning, evolution, and cognition. This theory has the characteristics of a great one; it is simple, general, falsifiable, and moreover seems probably, approximately, correct!”—Avi Wigderson, Nevanlinna Prize winner and Professor of Mathematics, Institute for Advanced Study, Princeton

“[Valiant] grounds his hypotheses in solid computational theory, drawing on Alan Turing’s pioneering work on ‘robust’ problem-solving and algorithm design, and in successive chapters he demonstrates how ecorithms can depict evolution as a search for optimized performance, as well as help computer scientists create machine intelligence.... [H]is book offers a broad look at how ecorithms may be applied successfully to a variety of challenging problems.”—Publishers Weekly